Non-Markovian Quantum Mpemba effect

Abstract

Since it's rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received significant attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this work, we consider a general non-Markovian open quantum setting and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Due to non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, therefore giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and non-equilibrium setups at weak, intermediate and strong coupling, and both with and without interactions. Our work provides new insights into the rich physics underlying accelerated relaxation in quantum systems.

v2, 4 pages, 3 figures and supplemental material. Substantially updated from v1

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• Symmetry restoration and quantum Mpemba effect in many-body localization systems
• Intrinsic Quantum Mpemba Effect in Markovian Systems and Quantum Circuits
• Pontus-Mpemba effects
• Tuning the Quantum Mpemba Effect in Isolated System by Initial State Engineering
• A simpler probe of the quantum Mpemba effect in closed systems
• Quantum Mpemba effect in long-range spin systems
• Speeding up Pontus-Mpemba effects via dynamical phase transitions
• Fast and direct preparation of a genuine lattice BEC via the quantum Mpemba effect
• The Mpemba effect in quantum oscillating and two-level systems
• Quantum Mpemba effect in parity-time symmetric systems
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• A resource theoretical unification of Mpemba effects: classical and quantum
• Quantum Mpemba Effect Induced by Non-Markovian Exceptional Points
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Emergent Liouvillian exceptional points from exact principles
• Robustness of the quantum Mpemba effect against state-preparation errors
• The Mpemba effect in the Descartes protocol: A time-delayed Newton's law of cooling approach
• Quantum Mpemba effect in chaotic systems with conservation laws